Convert the following predicate to one that has no negation in it. Justify each step.
¬∀x((P(x) ∨ S(x)) → ∃y(¬Q(x, y) ∧ ¬R(x, y)))
Convert the following predicate to one that has no negation in it. Justify each step. ¬∀x((P(x)...
Let P(X) be the predicate " is a dragon." Let Q(x) be the predicate "x breathes fire.” Let R(x,y) be the predicate "x and y are the same object.” Let S be an arbitrary nonempty set. Rewrite the following English statements in symbolic no- tation using predicates P, Q, R, universal and existential quanti- fiers, and any variables you want. i. There are no dragons in S. ii. Not everything in S is a dragon. iii. There is at least...
Simplify the following sentences in predicate logic so that all the negation symbols are directly in front of a predicate. (For example, Vx ((-0(x)) + (-E(x))) is simplified, because the negation symbols are direct in front of the predicates O and E. However, Væ -(P(2) V E(x)) is not simplified.) (i) -(3x (P(x) 1 (E(x) + S(x)))) (ii) -(Vx (E(x) V (P(x) +-(Sy G(x, y))))) Write a sentence in predicate logic (using the same predicates as above) which is true...
6. Consider the predicates M(x), F(x), and P(x, y) in a domain of people. The predicate M(x) states of a person that he is male, the predicate F(x) states of a person that she is female, the predicate P(z, y) states that x is the parent of y. Write the following queries in the Predicate Logic. (a) Find the people who are mothers (b) Find the people who do not have an uncle.
Give an example of a predicate P(x, y) such that the following two statements are logically equivalent: Vx3yP(x, y) and 3xVyP(x, y)
Module Outcome #3: Translate prose with quantified statements to symbolic and find the negation of quantified statements. (CO #1) Module outcome #3: Translate prose with quantified statements to symbolic negation of quantified statements. (CO #1) (a.) Negate the statement and simplify so that no quantifier or connective lies within the scope of a negation: (Bx)(y)-P(x.y) AQ(x, y)) (b.) Consider the domain of people working at field site Huppaloo, Let M(xx): x has access to mailbox y. Translate into predicate logic...
6. (4 marks) Write down the negation of each of the following statements. Then determine whether the statement or its negation is true, and explain why (a) x E R, y E R such that xy 5. (b) z, y E R+ such that V z E Z+, > z.
3. In the domain of all movies, let D(x) be the predicate "x has a demon in it." and P(x) be the predicate "x is about ponies." Which one of the following statements represents "Some movies that have a demon in it are not about ponies." (3 points] a. (3x)(D(x) → P(x)) b. (3x)(D(x) A-P(x)) c. (Vx)(P(x) →D(x)) d. (3x)(PD(x)) +-P(x))
Prove the validity of the following sequents in predicate logic, where F, G, P, and Q have arity 1, and S has arity 0 (a ‘propositional atom’):
Rewrite the following statement so that negations appear only within predicates (i.e., no negation or not is outside a quantifier or a compound statement using logical operators/connectives). Please write it clearly and show every step! V ((Vy32 -P(x, y, z)) 4 (3 z Vy R(x, y, z)))
question 5.20. Let P(x, y) be the predicate x + y = 10 where x and y are any real numbers. Which of the following statements are true? (a) (∀x)(∃y), P(x, y). (b) (∃y)(∀x), P(x, y)